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Dear Simon,

if you don't need an exact ROI of you object, you could use Plugins > 
Tracking > Manual Tracking to get the coordinates of your object over 
time quite conveniently. Then run the script below to get rectangular 
images following your manually tracked object (the tracking-result 
window should be the active window, when running the script).

IJ.renameResults("Results");
windowsize = 50; //size of cropped image in px
title = getTitle();
for (i=0; i<nResults; i++){
slice=getResult("Slice n°", i);
x=getResult("X", i);
y=getResult("Y", i);
run("Specify...", "width="+windowsize+ " height="+windowsize+ " x="+x+" 
y="+y+" slice="+slice+" centered");
run("Duplicate...", "title=croppedslice_");
selectWindow(title);
}
run("Images to Stack", "name=Stack title=cropped use");

Kind regards
Anna

On 2017-07-31 13:02, Simon Walker wrote:
> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> Post images on http://www.imgur.com and include the link in your 
> posting.
> *****
> 
> Dear List,
> This seems like a pretty basic problem, but I can't readily find a
> solution.  Is it possible in e.g. FIJI/ImageJ to crop around a moving
> feature to create a movie that will always have the feature of
> interest at its centre?  What I would ideally like is to specify e.g.
> 50x50 px ROI, manually position this over the feature of interest,
> click to select and export the selection to a new file, automatically
> advance to the next frame and repeat.  Ok, so I could write a script,
> but surely someone must have done this already??
> Thanks,
> Simon